Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (9+3*x^2+4*x)/(7-7*x+3*x^2)
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Limit of (1+2*n)/(-1+3*n)
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Limit of (x^3-3^x)/(-3+x)
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Limit of -x+(-2+x)^4/(3+x)^4
- Graphing y =:
- -cos(1/x)/x^2
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Identical expressions
- -cos(one /x)/x^ two
- minus co sinus of e of (1 divide by x) divide by x squared
- minus co sinus of e of (one divide by x) divide by x to the power of two
- -cos(1/x)/x2
- -cos1/x/x2
- -cos(1/x)/x²
- -cos(1/x)/x to the power of 2
- -cos1/x/x^2
- -cos(1 divide by x) divide by x^2
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Similar expressions
- cos(1/x)/x^2
Limit of the function -cos(1/x)/x^2
The solution
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[src]
/ / 1\ \
|-cos|1*-| |
| \ x/ |
lim |----------|
x->0+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right)$$
Limit((-cos(1/x))/(x^2), x, 0)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
One‐sided limits
[src]
/ / 1\ \
|-cos|1*-| |
| \ x/ |
lim |----------|
x->0+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right)$$
oo*sign(<-1, 1>)
$$\infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
= 3.96548889008278e-74
/ / 1\ \
|-cos|1*-| |
| \ x/ |
lim |----------|
x->0-| 2 |
\ x /
$$\lim_{x \to 0^-}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right)$$
oo*sign(<-1, 1>)
$$\infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
= 3.96548889008278e-74
= 3.96548889008278e-74
Rapid solution
[src]
oo*sign(<-1, 1>)
$$\infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = - \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = - \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = - \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = - \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = 0$$
More at x→-oo
The graph